Representing Topological Relationships between Complex Regions by F-Histograms

In earlier work, we introduced the notion of the F-histogram and demonstrated that it can be of great use in understanding the spatial organization of regions in images. Moreover, we have recently designed Fhistograms coupled with mutually exclusive and collectively exhaustive relations between line segments. These histograms constitute a valuable tool for extracting topological relationship information from 2D concave objects. For any direction in the plane, they define a fuzzy partition of all object pairs, and each class of the partition corresponds to one of the above relations. The present paper continues this line of research. It lays the foundation for generating a linguistic description that captures the essence of the topological relationships between two regions in terms of the thirteen Allen relations. An index to measure the complexity of the relationships in an arbitrary direction is developed, and experiments are performed on real data.